Get the Knowledge that sets you free...Science and Math for K8 to K12 students

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Co-ordinate Axes and Planes

To locate the position of a point in a plane (say X-Y which are mutually perpendicular intersecting lines), we require the two co-ordinates of the point with respective to the two co-ordinate axes. But in real life, in addition to points in a plane, we deal with points in a space - the locations of which depend on three co-ordinates. Ex: Central position of a ceiling fan in your class room, in which the height from the floor is also important.

Consider three mutual perpendicular planes intersecting at a point 'O'. These three planes intersect along the lines X'OX (called the X-axis), Y'OY (called the Y-axis) and Z'OZ (called the Z-axis). These three axes constitute the rectangular co-ordinate system.

Note: The XOY plane is considered as horizontal (say the plane of the paper). Then the line Z'OZ (which is perpendicular to the plane XOY) is the vertical.

The three co-ordinate planes are: XY-plane (XOY), YZ-plane (YOZ) and ZX-plane (ZOX). The point 'O' is called as the origin of the co-ordinate system. Refer above figure.

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Octants

The three co-ordinate planes divide the space into eight segments known as octants. Refer table below and the accompanying animation:

Octant Segment Octant Segment
I XOYZ V XOYZ'
II X'OYZ VI X'OYZ'
III X'OY'Z VII X'OY'Z'
IV XOY'Z VIII XOY'Z'
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Sign Convention

For the sign convention (positive or negative) for the distances measured from the three planes, refer to the below table and the animation in the adjacent figure.

Plane Direction Sign
XY upwards OZ Positive
XY downwards OZ' Negative
ZX right OY Positive
ZX left OY' Negative
YZ front OX Positive
YZ back OX' Negative